Suppose that the weight in pounds of an airplane is a linear

Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line with a slope of 6.2. See the figure below. With 53 gallons of fuel In its tank, the airplane has a weight of 2328.6 pounds. What Is the weight of the plane with 79 gallons of fuel in its tank?

Solution

The question is gased on the linear equation where slope has been provided as 6.2. So, we will use slope-intercept form of equaiton that is y = mx+b. Here, m represents the slope of the equation and b represents the y-intercept.

Here, m is given 6.2 so by plugging it gives us the equation y = 6.2x+b. Thus, x represents the amount of fuel (in gallons) and y is the weight (in pounds).

Given that the weight of the plane is 2328.6 pounds when the fuel in the tank of the plane is 53 gallons. So, we will plug x=53 and y = 2328.6 in the above equation and solve it for b.

We have 2328.6 = (6.2)*53 + b

2328.6 = 328.6 + b [6.2 * 53 = 328.6]

2000 = b [subtracting 328.6 both sides of the equation]

Plugging it in the equation y = 6.2x + b, we have the complete equation that is y = 6.2x + 2000.

Now, we are asked the weight of the plane when the amount of fuel is 79 gallons so, we will plug 79 in place of x and calculate for y.

So, we have y = (6.2) * 79 + 2000

= 489.8 + 2000

= 2489.8 pounds. Answer